INTEGRABLE EXPANSIONS FOR POSTERIOR DISTRIBUTIONS FOR A 2-PARAMETER EXPONENTIAL FAMILY

• 成果类型: Article
• 署名作者: SUN, DC
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176325758
• 发表日期: 1994
• 页码: 1808-1830
• 关键词: likelihood ratio; reference priors; weak expansions; inference; tests

摘要

Asymptotic expansions of posterior distributions are derived for a two-dimensional exponential family, which includes normal, gamma, inverse gamma and inverse Gaussian distributions. Reparameterization allows us to use a data-dependent transformation, convert the likelihood function to the two-dimensional standard normal density and apply a version of Stein's identity to assess the posterior distributions. Applications are given to characterize optimal noninformative priors in the sense of Stein, to suggest the form of a high-order correction to the distribution function of a sequential likelihood ratio statistic and to provide confidence intervals for one parameter in the presence of other nuisance parameters.